A novel design method based on flow pattern construction for flow passage with low flow drag and pressure drop

• A design method for flow passage is developed based on flow pattern construction.
• Flow pattern construction is considered as a variational problem.
• Virtual volume force is derived as the solution of the variational problem.
• Porous media model and VOF model combine in the construction process of flow pattern.

A novel design method for flow passage with low flow drag and pressure drop was developed based on flow pattern construction. The specific flow pattern with minimum viscous dissipation rate represents low pressure drop in the flow passage. Thus, the fluid flow requires to be optimized as a variational problem subject to the minimum viscous dissipation rate principle, which is also considered as flow pattern construction. By using calculus of variations, the governing equations for the construction of the specific flow pattern were derived from the functional extremum problem represented by the Lagrange multiplier equation. After that, a computational fluid dynamics model was set up and applied in the solution procedure of the governing equations to generate the geometry of the flow passages based on the flow pattern construction. As the illustrative examples to validate the proposed design method, the geometries of flow passages were optimized in terms of pressure drop in a wide range of Re numbers.